Finite Group DatabasebetaFinite Group Databasebeta| order | 2016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | ΓL(1,𝔽8)×#882 |
| Fitting | C3×C7×C22⋊C4 ⋊ C2×C3 |
| Hall | C3×ΓL(1,𝔽8) ⋊ #120 |
| Sylow | C7 ⋊ C3×#882 |
554 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
120 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id.